GRADING AND SCREENING 249 expected that the chafing and bending effect on the wires of the cloth tending to wear them at the crimping points or break them by repeated flexures would increase with the coarseness of the cloth used but at this writing there is no data available on this point. All these vibrating screens are more or less dependent on gravity as a progressive force, that is they are all more or less inclined. The rate at which the undersize passes down through the openings of screens would increasingly be diminished by friction as the openings diminish in size. If the apertures of a screen be considered as pipes for the transport of material then evidently even if the stock of which the screen is composed is reduced in thickness to a degree proportional to the width of the aperture, since the number of apertures per unit of surface increases as the reciprocal of the square of the opening, the opposition to discharge must increase as the linear number of meshes increases. As a matter of fact the ratio of the weight of stock in the screen per unit of area to the area of opening increases as the number of apertures per linear unit increases, and consequently the increase of friction as the size of the apertures is diminished is something more than can be expressed by a simple ratio. With screen cloth the percentage of net opening diminishes with reduction in the size of opening. Some idea of this can be gotten by comparing the extremes of the Tyler sieve scale. The screen of largest opening 1.050 in. has a wire of 0.149 in diameter. The 200-mesh screen has an opening 0,0029 and a wire 0.0021 in diamete: the first case the percentage of areal opening is about 77 per cent and in the secu~~ about 34 per cent. As is quite evident the decrease of open area with size diminishes the chances of the undersize grains passing through the apertures. When materials are comminuted or reduced in size by crushing, grinding, shredding or other similar operations the amount of oversize tends to increase from size to size as the sizes successively diminish and as the limit of crushing is successively diminished in size. This is due to the fact that each comminution or other reducing action adds a modicum of fines and the amount of the fines becomes greater with successive reducing actions. If the limit of reduction be high and the resulting mass of particles be subjected to screening operations on a battery of screens of the same size and shape, the undersizes passing to the screen next below in size, etc., there may not be sufficient material when the finer sizes are reached to load the corresponding screens to capacity. On the other hand if the material to be screened has been reduced to a fine state of division the proportioning of screen surface according to a diameter rule based on some higher upper limit of reduction will lead to under capacity. Cohesion and adsorption increase with reduction in size. When coarse sizes are being screened the eye will detect very quickly particles of undersize in the oversizes. With the fine sizes the eye will be ignorant of diameter variations as great 1000 per cent or even greater. In testing with hand screens with hand manipulation the individual screens are shaken until the eye is satisfied when fine sizes are being tested.1 With material IJ^in. size and larger it is a simple matter after shaking out the small undersize grains to pick up the individual pieces and try them in various axial position to see if they will pass the apertures. Below %-in. size this procedure is very arduous. On coarse material it is possible to obtain a perfect screen test but not on fine. With fine sizes since the eye is the final criterion of commercial screening much greater capacity is satisfactorily obtained than would be permissible if exact criteria of efficiency were used. Precise Screening.—It will be evident that with very little reduction in capacity per unit of width of screen but with increased length such length depend- i The undersize can be removed and the further amount screened out in a given time noted. This is done in cement testing.—EDITOR.